Adjustable focus eyeglasses

ABSTRACT

Adjustable focus eyeglasses with two lens units, each lens unit having two lens elements. The eyeglasses are focused by adjusting the position of at least one of the two lens elements relative to the other in a direction generally perpendicular to a viewing direction. The relative motion can be linear or pivotal about a pivot location outside the lenses. Applicant provides basic general equations defining the thickness profiles for the lenses and the solutions to these equations are:  
         t   =       A   ⁡     [       uv   2     +     2   ⁢     (       α   ⁢           ⁢   v     +   1     )     ⁢       (       α   ⁢           ⁢   u     -     sin   ⁡     (     α   ⁢           ⁢   u     )         )     /     α   3           ]       +       B   [     2   ⁢     (       α   ⁢           ⁢   v     +   1     )     ⁢       (     1   -     cos   ⁡     (   au   )         )     /     α   2         )     ⁢     ]       +       C   ⁡     (       v   ⁢           ⁢       sin   ⁡     (   au   )       /   α       -       (       α   ⁢           ⁢   u     -     sin   ⁡     (     α   ⁢           ⁢   u     )         )     /     α   2         )       ⁢     ]       +   Du   +   E   +     F   ⁡     (   v   )       +     F   ⁢           ⁢   1   ⁢     (     u   ,   v     )     ⁢     u   4       +     F   ⁢           ⁢   2   ⁢     (   v   )     ⁢     u   3     ⁢   v     +     F   ⁢           ⁢   3   ⁢     (   v   )     ⁢     u   2     ⁢     v   2       +     F   ⁢           ⁢   4   ⁢     (   v   )     ⁢     uv   3           ,       
where A for one of the lenses elements is −A for the other lens element in each lens unit and F(v), F1(u,v), F2(v), F3(v), F4(v) are any functions over the area of the lenses for which derivatives up to at least third order are continuous. At least one of F1(u,v), F2(v), F3(v), F4(v) is non-zero.

This application is a continuation in part of U.S. patent applicationSer. No. 11/085,436 filed Mar. 21, 2005 Ser. No. 11/243,944 filed Oct.5, 2005, Ser. No. 11/387,023 filed Mar. 21, 2006 and Ser. No. 11/580,398filed Oct. 14, 2006, each of which are incorporated herein by reference.This invention relates to eyeglasses, in particular to adjustable focuseyeglasses, and to processes for making adjustable focus eyeglasses.

BACKGROUND OF THE INVENTION Nearsightedness and Farsightedness

Nearsightedness is a condition of the eye in which distance objectscannot be focused on the retina and farsightedness is a condition of theeye in which near objects cannot be focused on the retina. Theseconditions are normally corrected by eyeglasses lenses having a powerneeded to correct the eye's focus error.

Astigmatism

Astigmatism is a condition of the eye caused by an irregular curvatureof an eye surface, usually the front surface. It can be corrected by aneyeglasses lens in which at least one surface has a different curvaturein different planes through the lens axis.

Thin Lenses

In ophthalmology and optometry it is customary to specify the focallength of spectacle lenses in diopters. The power P of any lens indiopters D is defined as the reciprocal of the focal length f in meters(i.e. P=1/f). For thin lenses, the power P of a two lens (P₁ and P₂)stacked combination is the sum of the power of the two lenses (i.e.,P=P₁+P₂) Stacking of two thin lenses 1 and 2 where P₁=−P₂ would producea power of zero, equivalent to a flat plate. The two lenses do notperfectly cancel, but as long as the power is fairly weak (i.e., lessthan about 5 diopters), the human eye does not detect the residualaberration.

The Human Eye

The adjustable lens of the human eye, called the “crystalline lens”, islocated immediately behind the iris. The crystalline lens is comprisedof 4 layers, from the surface to the center: the capsule, thesub-capsular epithelium, the cortex and the nucleus. The lens capsule isa clear, membrane-like structure that is quite elastic, a quality thatkeeps it under constant tension. As a result, the lens naturally tendstoward a rounder or more globular configuration, a shape it must assumefor the eye to focus at a near distance. Slender but very strongsuspending ligaments, which attach at one end to the lens capsule and atthe other end to protrusions of the circular ciliary body around theinside of the eye, hold the lens in place. When the ciliary bodyrelaxes, the protrusions pull on the suspending ligaments, which in turnpull on the lens capsule around its equator. This causes the entire lensto flatten or to become less convex, enabling the lens to focus lightfrom objects at a far away distance. Likewise when the ciliary musclecontracts, tension is released on the suspending ligaments, and on thelens capsule, causing both lens surfaces to become more convex again andthe eye to be able to refocus on near objects. This adjustment in lensshape, to focus at various distances, is referred to as “accommodation”.The “amplitude of accommodation” of an eye is the maximum amount thatthe eye's crystalline lens can accommodate. This amount is very highwhen young and decreases with age.

The cornea of the human eye is also important in providing focus. Infact, the cornea provides by far the greatest optical power in the eye,with a power of 43.0 D. The entire optical system of the eye has a powerof 58.6 D. This causes the light entering the eye to focus onto theretina. The power of the cornea cannot be adjusted, except by surgery.

Presbyopia

After age 40 in most people (and by age 45 in virtually all people) aclear, comfortable focus at a near distance becomes more difficult witheyes that see clearly at a far distance. This normal condition is knownas “presbyopia”, and is due both to a lessening of flexibility of thecrystalline lens and to a generalized weakening of the ciliary muscle.By the time one reaches 65 or so, the crystalline lens is virtuallyincapable of changing shape. Unless one is nearsighted, it is notpossible to focus objects (such as a printed page) clearly at even anarm's length distance. The amount of presbyopia inevitably increaseswith age. Eyeglasses are usually used to provide correct focus asneeded. These eyeglasses include bifocal, trifocal, and continuous focalglasses. Other solutions include separate glasses for distance andreading.

Attempts have been made to design glasses providing adjustable focus.Suggested techniques include: (1) pumping a clear fluid between thinlenses that bulge with increasing pressure (U.S. Pat. No. 2,567,581),(2) use of voltage controlled liquid crystal nematic material to changerefractive indexes (U.S. Pat. No. 5,359,444) and (3) use of a variety ofpixilated electro-active materials (U.S. Pat. No. 6,733,130). Theseprior art patents are incorporated herein by reference. These prior artpatents disclose techniques for finding automatic focus settings forthese glasses. These techniques include range finders and small cameraviewing of both eyes to detect distances being observed. These prior artpatents also describe small processors and drivers to control focusbased on estimates of the distances.

Bifocals, trifocal and continuous focus glasses all have their problemsas is well known by the people who wear them, and the automatic focusglasses have not been successful in solving the problems. Surgery cancorrect vision problems in many cases, but eye surgery is expensive andmany people who can afford eye surgery, prefer to avoid it.

Alvarez and Mukaijama Adjustable Focus Patents

Luis W. Alvarez patented an adjustable focus lens system in 1967 (U.S.Pat. No. 3,305,294) and another in 1970 (U.S. Pat. No. 3,507,565). Thesepatents describe lens systems comprised of two complementary lenses.Combining the two lenses produced a lens unit with a focus that could beadjusted by relative motion of the two lenses in an x direction (i.e.linear direction) perpendicular to a viewing direction. These adjustablefocus lenses have thickness t described by the equation:t=A(xy ²+⅓x ³)+Bx ² +Cxy+Dx+E+F(y),or equivalently the by system of relations:∂³ t/∂x ³=2A,∂³ t/∂x∂y ²=2A, and∂³ t/∂x ² ∂y=0.For this we define the direction away from the face to be the zdirection, the translation direction to be the x direction, and thenon-translation direction to be the y direction. With this, the lenspair has a variable optical power as we translate them differentially inx. This variable power is a function of the distance that we translatethe lenses. The deficiency with the Alvarez equations is that thedescription is too simple for optimal properties. While the equationsare accurate for the region directly in front of the eyes, the glassesare deficient in a number of important optical (especially off-axisimage quality) and other quality (such as thickness and weight) andaesthetic parameters.

A patent issued to Mukaiyama and others in 1997 (U.S. Pat. No.5,644,374) describes essentially the same invention but in a differentway. Applicant has determined that the optical performance for designsaccording to the teachings of this patent to be inadequate. That patenttreats the two lenses as if they behave independently, with power andastigmatism effects essentially summing. Applicant has found thisassumption to be highly inaccurate, except in the case of lenses thatare so weak that they are commercially uninteresting. Also, this patentteaches that the lines of constant power should be parallel and linear,which Applicant has found not to be at all true for an optimized design.

What is needed is a better technique for solving problems of human eyefocus including the problems associated with presbyopia that we will allencounter, if we live long enough.

SUMMARY OF THE INVENTION

The present invention provides eyeglasses with two lens units, each lensunit having two lens elements. A mechanism is provided to adjust theposition of one of the two lens elements relative to the other in adirection generally perpendicular to a viewing direction. In a preferredset of embodiments the relative motion is linear in a single directionand in another set of embodiments the relative motion is pivotal about apivot location outside the lenses. A specially designed thicknessprofile for the first lens element defines a first thickness profile anda thickness profile for the second lens element defines a secondthickness profile. The designs of the specially designed thicknessprofiles are chosen such that small adjustments of the relativepositions of the two lenses in directions perpendicular or approximatelyperpendicular to a viewing direction results in changes in the combinedfocus of the two lenses of the lens unit.

General Equations for Thickness Profiles

Applicant uses coordinates (u,v) in a plane perpendicular to the viewingdirection when looking straight ahead (“on-axis”). He calls this planethe “plane of the lens”. The origin point (u,v)=(0,0) is defined to bethe point directly in front of the pupil when looking straight ahead.This is convenient because users in general desire better performancewhen the eye is looking on-axis compared to looking at an angle(“off-axis”). The u-coordinate points in the direction of relativemotion of the lenses when in the null position. The v-coordinatedirection is orthogonal to the u-coordinate direction, but in the planeof the lens.

The motion of the lens can either be purely in the u-direction, orrotate around an axis located at (u,v)=(0,−r₀). Applicant uses aparameter α which is 0 in the case of translational motion, and 1/r₀ inthe case of rotation around an axis.

The basic general equations defining the thickness profiles are givenby:((αv+1)⁻²∂³ t/∂u ³+α(αv+1)⁻¹∂² t/∂v∂u)|_((u,v)=(0,0))=2A(∂³ t/∂v ² ∂u)|_((u,v)=(0,0))=2A((αv+1)⁻¹∂³ t/∂v∂u ²−α(αv+1)⁻²∂² t/∂u ²)|_((u,v)=(0,0))=0.The notation “(u,v)=(0,0)” indicates that the relations only hold forthe center point (u, v)=(0,0), but not necessarily outside of thatpoint. However, Applicant requires the thickness profile functions to becontinuous, and the derivatives up to at least third order to becontinuous. Applicant picks A for one lens to be the complement(negative value) of A for the other lens.

The solutions to these equations are:t = A[uv² + 2(α  v + 1)(α  u − sin (α  u))/α³] + B[2(α  v + 1)(1 − cos (α  u))/α²)] + C[v  sin (α  u)/α − (α  u − sin (α  u))/α²)] + Du + E + F(v) + F  1(u, v)u⁴ + F  2(v)u³v + F  3(v)u²v² + F  4(v)uv³,whereF(v), F1(u,v), F2(v), F3(v), F4(v)are any functions over the area of the lenses for which derivatives upto at least third order are continuous.Translation Only Designs:

In the case of translation only designs, α=0. Applicant has defined x=u,and y=v. He defines the origin x=0, y=0 to be the point directly infront of the pupil when looking straight ahead. The equations in thisform for the translation designs are:(∂³ t/∂x ³)|_((x,y)=(0,0))=2A,(∂³ t/∂x∂y ²)|_((x,y)=(0,0))=2A, and(∂³ t/∂x ² ∂y)|_((x,y)=(0,0))=0.Note that the Alvarez description referred to in the Background Sectionis the same at the center (x,y)=(0,0), but Alvarez also applies thisrestriction away from the center point whereas the present inventionconsiders a wide variety of parameters to optimize the design across theentire lens profile. As above Applicant picks A for one lens to be thecomplement of A for the other lens.

The solution is found by taking the limit as a 0 in the above thicknessexpression, which results in.t=A(xy ²+⅓x ³)+Bx ² +Cxy+Dx+E+F(y)+F1(x,y)x ⁴ +F2(y)x ³ y+F3(y)x ² y ²+F4(y)xy ³.

This can be seen as identical to the Alvarez except for the addition ofF1, F2, F3 and F4. These additional functions will be shown in thispatent to be important for optimized performance.

Designs including rotation:

The relative motion perpendicular to the viewing direction may alsoinclude rotation in the plane of the lens. In this case, at least one ofthe lenses pivots about a pivot location. For a good solution to exist,this must be outside of the lens perimeter.

For the pivot design, we will call r₀θ=u, and r−r₀=v, with r₀=1/α. Theorigin r=0 is the pivot point, and r=r₀, θ=0 is the point directly infront of the pupil when looking straight ahead. In this form, theequations are given byr ₀ ⁻¹(r ⁻²∂³ t/∂θ ³ +r ⁻¹∂⁷ t/∂r∂θ)|_((r,θ)=(0,0))=2Ar ₀ ⁻¹(∂³ t/∂r ²∂θ)|_((r,θ)=(ro,0))=2Ar ₀ ⁻¹(r ⁻¹∂³ t/∂r∂θ ² −r ⁻²∂² t/∂θ ²)|_((r,θ)=(ro,0))=0.

The solution in this form ist=Ar ₀[(r ² +r ₀ ²)θ−2rr ₀sin(θ)]+B2r ₀ r(1−cos(θ))+Cr ₀ [r sin(θ)−r ₀θ]+Dr ₀ θ+E+F(r)+F1(r,θ)r ₀ ⁴θ⁴ +F2(r)r ₀ ³(r−r ₀)θ³ +F3(r)r ₀ ²(r−r₀)²θ² +F4(r)r ₀(r−r ₀)³θ,

The terms have been defined so that the constants are the same as in thegeneral equation, but a shorter equivalent form provided below ispossible by redefining the constants:t=A′r ² θ+B′r cos(θ)+C′r sin(θ)+D′θ+E′+F′(r)+F1′(r,θ)θ⁴ +F2′(r)(r−r ₀)θ³+F3′(r)(r−r ₀)²θ² +F4′(r)(r−r ₀)³θ.

Choosing Parameters

The choice of parameters to the general solutions depends on desiredoptical performance, other restrictions such as minimum and maximumthickness and aesthetic and other considerations. These specific optimumsolutions use a form much more general than that described by Alvarez.Applicant picks the parameters and functions to optimize lensproperties. In preferred embodiments 17 specific parameters andfunctions are optimized to provide desired performance and other qualityand aesthetic results.

Adjustable Frame Designs

Several specific frame designs are described. For the linear relativemotion approach some designs provide for movement side to side movementof the lens elements relative to each other. In other designs therelative motion is up and down. Pivotable motion frame designs are alsodescribed. Techniques for automatic focusing of the lenses are alsodisclosed.

Fixed Lens Eyeglasses Utilizing the Present Invention

In other embodiments of the present invention, the lens units are firstadjusted relative to each other to provide a desired focusing power thenfixed in a frame to provide fixed lens units with a fixed power. Whenthe present invention is utilized to make fixed-lens eyeglasses, a verywide variety of lens powers can be produced with a minimal stock oflenses. Astigmatism may be corrected by a small adjustment in a seconddirection perpendicular to the first direction followed by a rotation ofthe two lenses about the axis of the two lenses. When the adjustmentshave been made the two lenses are fixed with respect to each other andinstalled in eyeglass frames. Cutting to the shape of the eyeglassframes can occur either before or after the fixing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A, 1B and 1C show relative movement of two lens elements in thevertical, horizontal and pivot directions.

FIG. 1D shows the general shape of preferred lens elements and an “eyecenter”.

FIGS. 2A, 2B and 2C and 3A, 3B and 3C show results achieved with thepresent invention.

FIGS. 4A, 4B and 4C show comparison results achieved with a prior arttechnique.

FIGS. 5A and 5B and 5A and 6B show features of another prior arttechnique.

FIGS. 7A and 7B show features of a frame design for horizontal relativelens motion.

FIG. 8 shows a frame design for vertical relative lens motion.

FIGS. 9A through 9I show features of a second frame design for verticallens motion.

FIGS. 10A through 10E show features of a third frame design for verticallens motion.

FIGS. 11A through 11C show features of a fourth frame design forvertical lens motion.

FIGS. 12A through 12D show features of a fifth frame design for verticallens motion.

FIGS. 13A through 13G show features of a frame design for pivotal lensmotion.

FIGS. 14A through 14G show features of a second frame design for pivotallens motion.

FIGS. 15A through 15H show features of a third frame design for pivotallens motion.

FIGS. 16A and 16B show a frame system for side to side adjustment.

FIG. 17 show results of a ZEMAX optimization.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Theory

In preferred embodiments of the present invention a mechanism isprovided to adjust the position of one of the two lens elements (in eachof the two lens units) relative to the other lens element in a directiongenerally perpendicular to a viewing direction. In a preferred set ofembodiments the relative motion is linear in a single direction and inanother set of embodiments the relative motion is pivotable about apivot location outside the lenses. Examples of this relative motion areshown in FIG. 1A (vertical motion), FIG. 1B (horizontal motion) and FIG.1C (pivotal motion). The first lens element has a specially designedthickness profile defining a first thickness profile and the second lenselement has a thickness profile defining a second thickness. Thethickness profiles are designed such that small adjustments of therelative positions of the two lenses in directions perpendicular orapproximately perpendicular to a viewing direction results in changes inthe combined focus of the two lenses of the lens units.

General Equations for Thickness Profiles

Applicant uses coordinates (u,v) defined in the plane of the lens. Theorigin point (u,v)=(0,0) is defined to be the point directly in front ofthe pupil when looking on-axis. This is convenient because users ingeneral desire better performance when the eye is looking nearer tostraight ahead. The u-coordinate points in the direction of relativemotion of the lenses when in the null position. The v-coordinatedirection is orthogonal to the u-coordinate direction, but in the planeof the lens.

The motion of the lens can either be purely in the u-direction, orrotate around an axis located at (u,v)=(0,−r₀). We will use a parametera which is 0 in the case of translational motion, and 1/r₀ in the caseof rotation around an axis.

The basic general equations defining the thickness profiles are givenby:((αv+1)⁻²∂³ t/∂u ³+α(αv+1)⁻¹∂² t/∂v∂u)|_((u,v)=(0,0))=2A(∂³ t/∂v ² ∂u)|_((u,v)=(0,0))=2A((αv+1)⁻¹∂³ t/∂v∂u ²−α(αv+1)⁻²∂² t/∂u ²)|_((u,v)=(0,0))=0.The notation “(u, v)=(0,0)” indicates that the relations only hold forthe center point (u, v)=(0,0), but not necessarily outside of thatpoint. However, Applicant requires the thickness profile functions to becontinuous, and the derivatives up to at least third order to becontinuous. He picks A for one lens element to be the complement of theother lens element.

The solutions to these equations are:t = A[uv² + 2(α  v + 1)(α  u − sin (α  u))/α³] + B[2(α  v + 1)(1 − cos (α  u))/α²)] + C[v  sin (α  u)/α − (α  u − sin (α  u))/α²)] + Du + E + F(v) + F  1(u, v)u⁴ + F  2(v)u³v + F  3(v)u²v² + F  4(v)uv³,whereF(v), F1(u,v), F2(v), F3(v) and F4(v)are any functions over the area of the lenses for which derivatives upto at least third order are continuous.

Translation only designs:

In this case α=0. Applicant defines x=u, and y=v. He defines the originx=0, y=0 to be the point directly in front of the pupil when lookingstraight ahead. The equations in this form are:(∂³ t/∂x ³)|_((x,y)=(0,0))=2A(∂³ t/∂x∂y ²)|_((x,y)=(0,0))=2A(∂³ t/∂x ² ∂y)|_((x,y)=(0,0))=0.Note that the Alvarez description is essentially the same at the center(x,y)=(0,0), but is too restrictive away from the center point.Applicant picks A for one lens to be the complement of the other lens.

The solution in found by taking the limit as a α→0 in the abovethickness expression, which results int=A(xy ²+⅓x ³)+Bx ² +Cxy+Dx+E+F(y)+F1(x,y)x ⁴ +F2(y)x ³ y+F3(y)x ² y ²+F4(y)³.This can be seen as identical to the Alvarez except for the addition ofF1, F2, F3 and F4. These additional functions will be shown in thispatent to be important for optimized performance.

Designs including rotation:

The motion we consider may also include rotation in the x-y plane. Inthis case at least one of the lenses pivots about a pivot location. Fora good solution to exist, this must be outside of the lens perimeter.

For the pivot design, we will call r₀θ=u, and r−r₀=v, with r₀=1/α. Theorigin r=0 is the pivot point, and r=r₀, θ=0 is the point directly infront of the pupil when looking straight ahead. In this form, theequations are given byr ₀ −1 (r ⁻²∂³ t/∂θ ³ +r ⁻¹∂⁷ t/∂r∂θ)|_((r,θ)=(0,0))=2Ar ₀ ⁻¹(∂³ t/∂r ²∂θ)|_((r,θ)=(ro,0))=2Ar ₀ ⁻¹(r ⁻¹∂³ t/∂r∂θ ² −r ⁻²∂² t/∂θ ²)|_((r,θ)=(ro,0))=0.

The solution in this form ist=Ar ₀[(r ² +r ₀ ²)θ−2rr ₀sin(θ)]+B2r ₀ r(1−cos(θ))+Cr ₀ [rsin(θ)−r ₀θ]+Dr ₀ θ+E+F(r)+F1(r,θ)r ₀ ⁴θ⁴ +F2(r)r ₀ ³(r−r ₀)θ³ +F3(r)r ₀ ²(r−r₀)²θ² +F4(r)r ₀(r−r ₀)³θ,

The terms have been defined so that the constants are the same as in thegeneral equation, but a shorter equivalent form is possible byredefining the constants:t=A′r ² θ+B′r cos(θ)+C′r sin(θ)+D′θ+E′+F′(r)+F1′(r,θ)θ⁴ +F2′(r)(r−r ₀)θ³+F3′(r)(r−r ₀)²θ² +F4′(r)(r−r ₀)³θ.

Choosing Parameters

The choice of parameters to the general solutions depends on desiredoptical performance, other restrictions such as minimum and maximumthickness and aesthetic and other considerations. These specific optimumsolutions use a form much more general than that described by Alvarez.Applicant picks the parameters and functions to optimize lensproperties. In preferred embodiments 17 specific parameters andfunctions are optimized to provide desired performance and other qualityand aesthetic results. These parameters are picked based factors thatmay include:

-   -   The variable optical power is adequate:        -   1. The on-axis optical power at the various settings            (translation distances) should meet the design constraints.        -   2. The off-axis optical power at the various settings may be            allowed to deviate within certain limits. The amount of            deviation will typically be allowed to increase as the            direction becomes more off-axis.    -   The optical performance at all power settings is adequate. This        corresponds to the level of residual aberration at best focus:        -   3. The performance should be particularly good on-axis.        -   4. The off-axis performance may be allowed to degrade within            certain limits. The amount of degradation will typically be            allowed to increase as the direction becomes more off-axis.    -   5. The motion for a given optical power should be minimized.        This is equivalent to maximizing the magnitude of the A        parameter.    -   6. There will be a minimum lens thickness required for        manufacturability and safety.    -   7. The total weight of the lens should be minimized.    -   8. The shape of the front surface most away from the eye meets        certain aesthetic constraints such as a general convex shape.    -   9. The lenses are adequately separated so as not to bump.    -   10. The lenses are not allowed to separate so much as to make        the assembly significantly less aesthetic.    -   11. The inner surface closest to the eye is adequately separated        from the eye. The outer surface may also be constrained to be        within a certain distance of the eye for aesthetic reasons.    -   12. The “average” wedge, which causes a lateral shift in the        image location and possibly chromatic aberration, may be        constrained to be within a certain limit.    -   13. The variable wedge, which causes a lateral shift in the        image location as the power is adjusted, may be constrained to        be within a certain limit    -   14. The wedge, both static and variable, may be matched for the        lens pairs in front of each eye.    -   15. The design should be reasonably insensitive to the exact eye        location relative to the lens within certain limits. This is to        accommodate different face shapes.    -   16. The design may contain a prescription base correction. This        base correction should be preserved as the lenses are translated        into their power settings.    -   17. There may be a surface that is manufactured to a stock        shape, with other surfaces allowed to be designed differently        for various designs. This is in order to reduce manufacturing        costs.

The thickness of the lens element in the above discussion is consideredto be the difference in the front surface and rear surface lensz-location defined as a function of x,y (or u,v or r,θ). Due to bowingor tilting of the lens, there will be a slight difference between thisthickness and thickness alternatively defined as minimum surfaceseparation. It is more conventional in manufacturing to use thez-location definition. While it is important to have the definitionclear for manufacturing, the effect on the constraints is usually veryminor. This is because specifically for eyeglasses, the lenses are closeenough to planar so that minimum thickness is close for the twodefinitions. The same discussion above also applies to gaps, which canbe thought of as airspace thickness.

In addition to thickness, which is the difference between the surfaces,the lens design also requires the average of the two surfaces to bespecified, which can be called the shape. Applicant places norestrictions on the functional form of the shape, other than the aboveconstraints, and limits to the degree of approximation (forcomputational purposes). In preferred embodiments actually tested withoptical software the constraints were applied with results that arediscussed later.

Balancing Design Constraints

All of these design constraints cannot simultaneously be individuallyoptimized; instead, some balance needs to be chosen by the designer.This can be accomplished algorithmically by combining constraints, forparameters which must be met; and a merit function to be minimized,which contains a functional combination of parameters and creates anoptimal balance based on the weighting of the parameters in the meritfunction.

Adequate Optical Performance

Adequate optical performance is both a design and a manufacturingconsideration. For the case of design, most common is to use thewell-known technique of ray tracing to evaluate performance. Othertechniques include wave optics simulations.

Adequate optical design performance divides into categories:

-   -   1. Optical power at the various settings, on-axis: usually        selected by the designer. This is the amount of focus, usually        expressed in diopters, of the rays entering the eye's pupil.    -   2. Optical power off-axis: this value should match the on-axis        power setting to a degree, but may be allowed to deviate in        order to optimize other lens parameters    -   3. Residual best-focus aberration, no prescription: minimized.        This is the residual ray angular deviation which remains after        focus is removed. The residual aberration will usually be most        constrained on-axis, and allowed to increase as the eye is        pointed increasingly off-axis. This can be expressed in terms of        peak aberration, or in terms of some weighted sum such as rms        aberration.    -   4. The residual best-focus aberration may be designed for a        prescription correction. In this case the residual will be        residual ray angular deviation which remains after focus and        prescription are removed. Usually the prescription correction        includes focus and 2 directions of astigmatism, but may include        higher order terms.        Preferred Technique for Optimization

Applicant presents here a preferred technique for optimizing the lensunits. It should be noted that the numerical techniques involved arestandard, and can be implemented in various ways. Elements of thepresent invention include the application of the desired constraints andmerit functions to the mathematics of lens design, and the more generalvariable thickness profile formulas which allow superior optimization.

As an example for a preferred embodiment, Applicant takes the followingparameters:

-   -   1. first lens height H1=36 mm,    -   2. second lens height H2=32 mm,    -   3. lens width W=50 mm,    -   4. lens perimeters shown in FIG. 1D,    -   5. eye center offset y=3 mm from lens center, plotted with a        cross in the FIG. 1D,    -   6. lenses translated in the height direction,    -   7. minimum thickness 1 mm for each lens,    -   8. index of refraction n=1.5,    -   9. motion of lenses +−1 mm complementary motion,    -   10. lens motion centered around an axis 150 mm behind lenses,        causing a slight rotation in the x-z plane in addition to the        translation,    -   11. 1 diopter base power for the system,    -   12. variable power +−1 diopter for the system,    -   13. total power 0 to 2 diopters,    -   14. center of lenses 35 mm from the eye center of rotation,    -   15. pupil diameter 4 mm,    -   16. total wedge less than 0.04,    -   17. 5 front surface locations defined for aesthetic reasons to        control the general curvature,    -   18. minimum lens separation 0.25 mm,    -   19. maximum lens separation 1.75 mm,    -   20. thickness restricted to x,y thickness equations defined        above, with terms up to 5^(th) order, and    -   21. shape allowed to be any 5^(th) order polynomial meeting the        above constraints.

Given the above constraints, Applicant investigated balance between theresidual aberration at various angles and the total weight, expressed asaverage thickness. He wanted to achieve:

-   -   1. average thickness <2 mm, or best possible,    -   2. single-wavelength ray aberration diameter <1 mrad at all 0.5        radian off-axis look angles, which corresponds to approximately        ½ diopter of astigmatism, or best possible, and    -   3. single-wavelength ray aberration diameter <⅓ mrad at all 0.25        radian off-axis look angles, which corresponds to approximately        ⅙ diopter of astigmatism, or best possible.

Applicant found it desirable to use a ray trace algorithm to evaluatethe residual aberration. The residual aberration was computed as theangular error remaining in rays throughout the pupil area, after thebest focus term is found and removed. He picked surfaces defined bypolynomials up to 5^(th) order, but constrained by the basic thicknessequation and the above constraints.

Lens thickness was evaluated at 211 points distributed throughout thelens to make sure that the minimum thickness was greater than 1 mm.These points were densest on the actual perimeter, because most of theminima are found on the perimeter. Gap thickness was evaluated at 61points for each of the 2 extreme translation positions. It should benoted that there are other numerical and analytic techniques to find theminimum and maximum thickness locations. Any of those techniques can beused to find minima, which are then used in the later optimization toprovide constraints on the optimization. Applicant has implemented thosetechniques, which also work, but seem to be numerically slower.

Applicant found it also desirable to evaluate the aberrations at 16positions placed in a circle for each of the two off-axis-angles (atotal of 32 directions), and for each of the two extreme lens positions.As explained above he picked surfaces defined by polynomials up to5^(th) order, but constrained by the basic thickness equation and theabove constraints. It is possible to use even higher order polynomials,and achieve better results; however, this requires more sampling of lookangles and thickness locations, and therefore increases computationalburden.

These calculations were carried out using MathCAD, with its built-inminimization routines. The MathCAD algorithms Applicant used are allstandard and well-known.

Chromatic aberration depends mostly on the power and wedge, so was notincluded in this optimization. The chromatic aberration has beenincluded in other designs we have performed using the commercial opticsdesign program Zemax. The Zemax optimizations will be discussed later.

Nominal Optimized Design:

This design used the general thickness equations described above.Polynomial terms up to 5^(th) order were considered for the thicknessprofiles. Applicant achieved:

-   -   1. average thickness 2 mm,    -   2. single-wavelength ray aberration diameter <0.84 mrad at all        0.5 radian off-axis look angles, and    -   3. single-wavelength ray aberration diameter <0.28 mrad at all        0.25 radian off-axis look angles.        The general shape of preferred lens elements are typical shapes        as shown in FIG. 1D.

The aberration diagrams are shown in FIGS. 2A, 2B, and 2C for the 0diopter, 1 diopter, and 2 diopter positions, respectively. The outerring of spots corresponds to 16 positions each 0.5 radian off-axis, andthe next ring corresponds to 16 positions each 0.333 radian off-axis,the inner ring is 0.166 radian off-axis, and the center spot is on-axis.These spots have been placed artificially close together for viewingpurposes. The spot sizes are plotted accurately on the scale where thegrid spacing equals 1 mrad.

The power diagrams are shown in FIGS. 3A, 3B, and 3C for the 0 diopter,1 diopter, and 2 diopter positions, plotted over the 0.5 radian nominalfield. The values are in diopters.

Achieving the proper on-axis power is important, and is constrained byfixing the A parameter; but a small deviation when looking off-axis isnot as important (as the eye usually is able to correct small focuserrors), and was not constrained in this case.

Optimization with a Prescription Function:

A design with prescription correction can be optimized using the sameprocedure described above. The only difference is subtraction of the raydirections associated with the desired base prescription before findingthe best focus residual aberration.

Optimization with a Pivot Design:

A pivot design is optimized using the same procedure described above fortranslating lenses. The only difference is 1) the lens thicknessparameters use the formula described above for the pivot design, and 2)the ray trace calculations and spacing calculations are performed on thelenses with the pivot motion rather than translation motion.

Comparison with Prior Art Designs:

Applicant prepared a prior art dedsign for comparison purposes. Thisdesign used the more restrictive thickness equations described inAlvarez, but with polynomial terms up to 5^(th) order considered for thecommon shape of the front and back surfaces. This allowed complex shapesbut with the simpler Alvarez thickness formula. Applicant achieved:

-   -   1. average thickness 2.22 mm,    -   2. single-wavelength ray aberration diameter <1.20 mrad at all        0.5 radian off-axis look angles, and    -   3. single-wavelength ray aberration diameter <0.40 mrad at all        0.25 radian off-axis look angles.

The results are shown in FIGS. 4A, 4B, 4C. Despite being significantlythicker and therefore more massive, the design has worse opticalperformance due to the restrictions on the thickness.

Optimized Design Matching Prior Art Thickness

This design used the general thickness equations described in thispatent. Polynomial terms up to 5^(th) order were considered for thesurfaces. The merit function was adjusted so that the average thicknessmatched the prior art design. We achieved:

-   -   1. average thickness 2.22 mm,    -   2. single-wavelength ray aberration diameter <0.42 mrad at all        0.5 radian off-axis look angles, and    -   3. single-wavelength ray aberration diameter <0.14 mrad at all        0.25 radian off-axis look angles.        Optimized Design Matching Prior Art Aberration:

This design used the general thickness equations described in thispatent. Polynomial terms up to 5^(th) order were considered for thesurfaces. The merit function was adjusted so that the residualaberrations matched the prior art design. Applicant achieved:

-   -   1. average thickness 1.88 mm,    -   2. single-wavelength ray aberration diameter <1.20 mrad at all        0.5 radian off-axis look angles, and    -   3. single-wavelength ray aberration diameter <0.40 mrad at all        0.25 radian off-axis look angles.        Summary: Alvarez and Mukaiyama vs Present Invention        Alvarez

The performance comparison of a lens unit designed according to thepresent invention versus an Alvarez designed lens unit is summarized inthe following table: Average Aberration Aberration Thickness (At 0.5Radians) (At 0.25 Radians) Prior Art (Alvarez) 2.22 1.20 0.40 PresentInvention 2.00 0.84 0.28 (Nominal) Present Invention 2.22 0.42 0.14 (LowAberration) Present Invention 1.88 1.20 0.40 (Low Weight)

It is clear that the equations described by Alvarez are significantlyinferior to the equations described in this patent.

Mukaiyama

The Mukaiyama patent (1997) treats the two lenses as if they behaveindependently, with power and astigmatism effects essentially summing.Applicant found this assumption to be highly inaccurate. To show this,he first plotted the power diagrams for the back and front lensseparately. See FIGS. 5A and 5B. Notice that the lines of constant powerare not even close to linear, in contrast to a key requirement of theMukaiyama patent.

Also, the Mukaiyama patent makes an implicit assumption that thesevalues simply add together when the lenses are placed in tandem. Here heshows that assumption to be false. See FIGS. 6A and 6B. The first plotis the sum of the above two power diagrams, with contour lines separatedby 0.05 diopters (the numbers were left off for visibility). The secondplot is the actual power diagram for the system. Notice that the twodiagrams do not agree, which shows that it is necessary to consider thelenses as a unit when performing the optimized design.

Zemax Optimization

ZEMAX optical design software was also used to perform the optimizationof the shape of the polynomial surfaces after the thickness profiles hadbeen calculated as described above. The optimization feature in ZEMAXuses an actively damped least squares method and a merit function thatallows for constraints on most optical and physical properties of alens. A root mean square (RMS) spot radius ‘Default Merit Function’ wasused with the additional constraint on the minimum lens thickness of 1.0mm. Due to the non-rotationally symmetric nature of these lenses,multiple operands were required to constrain the lens thickness atseveral radial zones within the lens. The nominal polynomial functionthat provides a desired change in optical focusing power with lateraltranslation tends to have thickness minima in the outer half of thelens, so the constraint on the minimum thickness was defined at zones of60%, 70%, 80%, 90% and 100% of the lens diameter.

A total of 27 configurations were created in a ZEMAX file to model thelens at 9 different eye gaze angles for 3 different lens translationalpositions (0D, +1D, +2D). The merit function was weighted over these 27positions such that the performance was appropriately better at thecentral gaze angles. Specifically, the on-axis gaze angle was weightedat 20, the next 4 closest gaze angles were weighted at 2 and the 4peripheral gaze angles were weighted at 1.

The thickness of the polynomial surface is defined by a 5^(th) orderpolynomial function in x and y. The form of the polynomial function is:T(x,y)=a ₁ x+a ₂ x ³ +a ₃ xy ² +a ₄ y ⁴ +a ₅ x ² y ² +a ₆ y ⁴ +a ₇ x ⁵+a ₈x³ y ² +a ₉ xy ⁴.In addition to slight eye focus for the off-axis gaze angles, thefollowing polynomial coefficients were free to vary during optimization:a₁, a₂, a₃, a₄, a₅, a₆, a₇, a₈, a₉.

The ratio of a₂ to a₃ was fixed to match the functional form definedabove for the thickness. Only even-powered y terms-were used because forthis particular case the lens and view angles were taken to be symmetricin y. This simplified the problem by introducing symmetry. The secondorder terms were omitted, because the lens surface radii of curvaturewere selected as an alternative to use of x² and y² terms.

FIG. 17 is the resulting spot diagrams for the 27 configurations. Theconfigurations correspond to the following lens positions and gazeangles:

Configurations 01-09=+1D

Configurations 10-18=+2D

Configurations 19-27=0D

On-Axis (OA) Gaze Angles=Configurations 1, 10, 19

Intermediate Gaze (IG) Angles=Configurations 2-5, 11-14, 20-23

Peripheral Gaze (PG) Angles=Configurations 6-9, 15-11, 24-27

Frame Designs

First Frame Design

A first proposed version of a frame design that permits lateral relativemotion of the lens elements in each lens unit is shown in FIG. 7A. Thisis a drawing of a pair of eyeglasses with wearer operated focusinglenses. A more detailed version of one of the lens units is shown inFIG. 7B. This embodiment includes metal or plastic frame 2, two backlenses 4 and two front lenses 6. Back lenses 4 are mounted rigidly onframe 2. Front lenses 6 are mounted so that they can be moved laterallywith respect to back lenses 4. Two pen mounts 8 are attached rigidly toframe 2 and tabs 10, 12 and 14 are attached rigidly to front lenses 6.Pen 16 passes through pen mounts 8, allowing it to slide through tab 10.Pen 18 passes through frame 2, allowing it to slide through tab 12.Adjustment screw 20 passes through frame 2 and screws into treadedsocket 15 in tab 14. Spring 22 between frame 2 and tab 12 provides acompressive force in the direction of adjustment screw 20. The wearer ofthe glasses shown in FIG. 7A adjusts the focus of each of the lenses byrotating adjustment screws 20 as shown in FIG. 7B.

Techniques for Use

This simple preferred embodiment of the present invention providesimportant improvements over prior art glasses such as bifocals,trifocals and continuous focal lenses. The lens units can each beadjusted by the user so that his viewed object at any distance from afew inches to infinity is exactly in focus. This is especiallyadvantageous if the viewed object is stationary with respect to thewearer such as when reading, working at the computer, watching TV andwatching a movie. Many of the potential embodiments of the presentinventions do not provide for very quick adjustment of the focus. Thiscould be somewhat of a problem in situations, for example, when astudent is watching a lecturer and taking notes at the same time. Asimple solution in these situations, however, would be to provide forseparate adjustment of the two lens units and for the wearer to adjustone lens units to focus on the lecturer and the other lens units tofocus on his notes. His brain will then take over and in each caseproduce images using data from the in-focus eye.

Movement Directions

The lenses can be moved separately or as units. Either lens of a lenspair can be moved, but the preferred approach is to move both lenses inopposite directions to achieve maximum differential movement with aminimum of absolute movement. In addition, the lenses can be adjustedusing actuation from both sides simultaneously, one particular sideonly, or either side. Designs which can be actuated from either sideallow the most ergonomic operation, and such designs with this propertyare described below.

FIG. 1A shows lens movement in the vertical direction. In this case thefront lens element can be moved as a unit, and the back lens elementmoved as a unit. Applicant discusses a variety of approaches toconstrain the motion to the proper displacement.

FIG. 1B shows lens movement in the horizontal direction. In this casethe front lens element can be moved as a unit, and the back lens elementeither fixed or moved as a unit; however, for this case it may bepreferable to connect one front lens to the back lens on the other eye,and vice versa (“crossover”). The crossover movement keeps the motionmore symmetrical between the two eyes.

FIG. 1C shows pivot motion. In this case, as in the horizontal motioncase, the front lens element can be moved as a unit, and the back lenselement either fixed or moved as a unit; however, for this case it maybe preferable to connect one front lens to the back lens on the othereye, and vice versa. The crossover pivot keeps the motion moresymmetrical between the two eyes.

Vertical Movement to Adjust Focus

There are some significant advantages of using vertical adjustment ofthe two lens elements relative to each other to provide focus changes.The principles described above for horizontal adjustment apply equallywell for the vertical adjustment, by interpreting x as the verticaldirection and y as the horizontal direction.

A frame design for vertical relative motion is shown in FIG. 8. In thisdesign, rear frame 100 is positioned on a wearer in the same manner asregular glasses. Front frame 102 is mounted on frame 100 with slideguide 106 and slide slot 108 so that front frame 102 is free to slide upand down relative to rear frame 100 but can not move sideways relativeto rear frame 100. The wearer is able to position front frame 102relative to rear frame 100 by pushing on actuating tab 104 in order toadjust the focus of the lenses. Close tolerances between guide 106 andguide slot 108 hold the front frame in position after it has beenpositioned by the wearer.

FIGS. 9A and 9B show another frame design for adjusting the front frameup and down relatively to the rear frame. In this case slide ring 110that is a part of front frame 116 slides up and down on shaft 112 thatis a part of rear frame 114. The wearer adjusts the relative positionsof the two frames by adjusting pivot bar 118. The earpieces 120 are apart of rear frame 114 and the nose rest 122 is a part of front frame115. Front frame 115 hangs from pivot bar 118 via hang element 121 thatpivots about pivot bar 118 and a pivot connection at nose rest 122 sothat the displacement of frame 116, produced by the pivoting of pivotbar 118, does not alter the spacing between the two frames.

FIGS. 9C through 9I show features of a frame design similar to the onedescribed-above. This frame includes back lens assembly 124, front lensassembly 126, a torsion bar assembly 128, two adjusting side bars 130and a nose piece assembly 132 and ear piece 134. The torsion barassembly includes torsion bar 128A two sleeves 128B (through which bar128A is free to pivot) that are rigidly attached to back lens assemblyat locations 128C. Bar 128A is pivotably attached to front lens frameassembly 126 at locations 128D. The two adjusting side bars 130 arepivotably attached to ear piece 134 at location 134A and are attached tofront lens assembly at location 134B as shown in FIG. 9G. Back lensassembly 124 includes peg attachment 124A which is comprised of twocurved pegs as shown in FIG. 9H. Front lens assembly 126 includes twosleeve attachments 126A each attachment having two sleeves that slide ina general up and down direction on the pegs of peg attachment 124A.Preferably the curve of the pegs matches the nominal radius of curvatureof the lenses. This frame also includes nose piece assembly 136 on whichboth front and back lens assemblies rest via sleeves 124B and 126B andstops 136A. With this feature the eyeglasses are positioned based on thelocation of the lowest of the two lens assemblies. Therefore, themovement of the center of the lens units relative to the wearer's eyesmoves only half as far as in the FIG. 8 example. Front lens assembly 126is raised relative to back lens assembly 124 by squeezing bar 130 andearpiece 134 at location 134A and lowered by squeezing at 134B as shownin FIG. 9G. Torsion bar 128 is preferably stiff enough to assure thatthe relative motion of the lens elements in both lens units isapproximately the same. The movement up or down of the front lenselements in one of the lens units relative to the rear lens elementinduces a torque on torsion bar 128A which produces a correspondingmovement in the front lens element in the other lens unit.

FIGS. 10A through 10E show features of a prototype frame design. In thisversion support frame 74 fits on the wearers head just as regularglasses. The lenses, both rear lenses 98R and 98L and front lenses 96Rand 96L are contained in separate frames, rear frame 72 and front frame70, that move relative to support frame 74. Frames 70 and 72 pivot aboutleft and right pivot mounts (left mount 92L and pivot screw 94L areshown). FIG. 11B shows the two lenses aligned. The wearer raises frontlenses 96L and 96R in front frame-70 and lowers rear lenses 98L and 98Rin rear frame 72 to positions such as the one shown in FIG. 11A bysqueezing frame temple arms at position 87 as shown in FIG. 11B. Thewearer moves the lenses in the opposite directions by squeezing frametemple arms at position 85 as shown in FIG. 11B. The result is shown inFIG. 11C.

FIGS. 12A through 12D shows a variation of the FIGS. 10A-E version. TheFIGS. 12A-D version is the same as the FIGS. 10A-E version except thewearer adjusts the relative positions of the lenses by turning cam 60instead of squeezing the temple arms.

Direction of Lens Movement

Preferably the relative motion of the two lens elements in a lens unitis in directions related to the nominal curvature of the lens unit. Forexample if the nominal curvature of the lens unit is 150 mm; theirrelative motion preferably could be along a radius approximately 150 mmbehind the center of the lens unit. However, optical analysis performedby Applicants has shown that tolerances on this issue is loose and (forthe 150 mm nominal curvature example) the lens unit performs acceptablyif the radius is within the range of about 50 mm to infinity (parallelmotion). For embodiments where the nominal curvature of the lenses isflat, relative motion should be parallel. In the examples shown in FIGS.10A through 10E the relative motion of the two lenses is defined byradii of about 50 mm. In the FIG. 8 example a curvature such as 150 mmcould be designed into guide 106 and guide slot 108. In the 9A and 9Bexample the shaft 112 and sleeves 110 could be designed for a curvatureof 150 or any other desired curvature.

Horizontal Movement to Adjust Focus

An example of horizontal motion frames is shown in FIGS. 16A and 16B. Inone of the units, the left rear lens is attached to the right frontlens, an earpiece, and a nosepiece. An identical but mirror-image unitis attached to this unit via a sleeve, allowing horizontal motion.

Pivot Adjustments of Focus

Eyeglasses made with lens pairs that are differentially rotated around apivot point outside of the lenses. The rotation is in a rotation planeapproximately perpendicular to the axes of the lenses and about a pivotpoint in the rotation plane. In embodiments of the present invention thesurface design of the lenses is much more complicated than in theAlvarez type embodiments and the designs described in the parentapplications referred to in the opening sentence of this specification,but the mechanism to move the lenses to achieve desired focusing powerturns out to be simpler and more precise as compared to the linearmovements. The pivot point is preferably equidistant from the two eyes.This preferred rotation point can be the midpoint between the two eyes,or any point above or below the midpoint.

Angular Adjustment with Crossover Pivot Mechanism

FIGS. 13A-13G are drawings showing features of a preferred embodimentproviding angular adjustment of the lenses of a set of eyeglasses usinga crossover pivot configuration. In this configuration the lenses pivotabout a pivot mechanism 150 identified in FIGS. 13B and 13G. Nose pieces152 are attached rigidly to pivot axle 154 in pivot mechanism 150. Allfour lenses pivot about pivot mechanism 150. Right front lens 156 isrigidly attached to left rear lens 158 and left front lens 160 isrigidly attached to right rear lens 162 so the lenses move in ascissors-like manner about pivot mechanism 150. The pivot mechanism 150and the connections to the lenses and nose piece are shown in FIG. 1G.Each of the two ear supports 164 attach to one of the rear lenses in themanner shown in FIG. 13D.

Angular Adjustment with Pivoting Front Lenses

FIGS. 14A-14G are drawings showing features of a preferred embodimentproviding angular adjustment of the lenses of a set of eyeglasses wherefront lenses pivot relative to back lenses. In this embodiment both rearlenses are rigidly attached to the nose piece and hinge-like to earsupports 164. The front lenses pivot about pivot 150A. Tab units 166attached to the front lenses limit range of movement of the frontlenses.

Angular Adjustment with Special Pivot Mechanism

FIGS. 15A-15H show detailed design features of a preferred embodimenthaving a special pivot mechanism that can be easily disassemble topermit cleaning of the lens elements. In this design, which is similarthe design shown in FIGS. 13A-13G, the pivot mechanism (as shown in FIG.15H) is provided by two half-sleeves 166 and 168 which are trapped byfront cap 170 and which rotate about a rotation base 172 that is fixedto nose piece 174, with the right front and left rear lens elementsrigidly attached on one half-sleeve and the left front and right rearlens elements rigidly attached on the other half-sleeve. The sleevesbeing trapped by the base and the end cap can only rotate. Some frictionis preferably built in to hold the positions of the lens elements whenno force is being applied. Additional friction can be applied bytightening Philips screw 176 which can also be removed to permitdisassembly and cleaning the inside surfaces of the lens elements.

Advantages of Adjustment about a Pivot Point

The special surface design to provide adjustable focus about a pivotpoint is quite a bit more complicated than the surface design for alinear adjustment. However, as indicated in FIGS. 13A-13G movement ofthe lenses about a pivot point greatly simplifies the frame design toaccomplish the relative lens movements as compared to sliding the lenseslinearly in a linear direction as proposed in Alvarez patents. With thepivot type embodiments, existing frame designs can be used along with asimple pivot type mechanism as shown in FIG. 13G. The pivot design asshown in FIG. 13A-13G assures that all relative movements are perfectlysymmetrical. This is difficult to accomplish with the linear motiontechniques.

Automatic Adjustments of Focus

Several prior art patents have proposed techniques for automaticadjustments of the focus of eyeglass lenses. These techniques attempt todetermine the distance to the viewed object and then automaticallyadjust the focus of the lenses in the eyeglasses based on storedinformation so that the object is in focus for the wearer. Thesetechniques include range finders and small camera viewing both eyes todetect distances between the pupils and small processors and drivers tocalculate distances and control focus based on the calculated distances.Cues from the wearer can also be used as a signal to provide anautomatic adjustment of the focus. For example, a wink of only the righteye could be a cue to increase the length of focus and a wink of onlythe left eye could be a cue to decrease it. Head motion or eyebrowmotion could also be used as a cue. Additional equipment would have tobe added to the basic embodiment described above. Needed would be amotor and actuator with a power source to provide the lateraldisplacement provided in the example by adjustment screw 20. A smallprocessor could be used to translate cues provided by the range finder,camera or wearer into instructions for the motor and actuator. Specificequipment of this general type for determining distances to viewedobjects is described in the patents referenced in the backgroundsection.

As an example, a system can be used to measure inter-pupil distance.This system would provide a determination of the distance of the objectthat the eyes are pointed at. If an object is far away, each eye ispointed in approximately the same direction. As the object moves closer,the eyes start to cross so that both are pointed at the object. Smallcameras can take digital images of each of the eyes and a miniaturedigital processor can compute the offset distance that maximizes thecorrelation of the two images. This offset, when added to the cameraseparation, yields inter-pupil distance. This inter-pupil distance canbe converted by the same digital processor into a range to the object,which is then converted to an offset distance for the sliding lenses.The processor then commands the motor/actuator to position the lenses inthe proper position.

Using the Present Invention to Make Fixed-Lens Eyeglasses

The techniques described in that application can be applied to greatlyreduce the cost of providing eyeglasses. These techniques reduce neededinventory stocks of lenses to meet patient's needs for focus andastigmatism correction. These techniques are described below:

Sets of lenses are prepared as described in the parent application,except the lenses are set during a second stage of a manufacturingprocess and not adjusted. The objective of this is to be able tomanufacture many different lens prescriptions with a small number ofparts. The parts will be able to cover a range of focus settings.Preferably there will be relatively small number of certain, coarselyspaced, focus powers on lens pairs that are maintained in stock.Applicant believes that most eye-care facilities will choose to stockabout 10 to 20 different focus power lens pairs. Fine-tuning will beaccomplished by displacing the two lenses in the lens pair. The lenspair is then cut and placed into the frames. This process provides forthe correction of focus but not astigmatism.

To also provide for the correction of focus and astigmatism a lens pairclosest to the desired focus power is chosen from stock as describedin 1) above. Adjustments are made in a first direction (the x-direction)to provide the desired focus. Then adjustments are made in a y-directionperpendicular to the x-direction to apply astigmatism correction to thelenses. In this case, we need to add a fourth equation to the previousthree equations in the translating x-y form:(∂³ t/∂x ³)|_((x,y)=(0,0))=2A,(∂³ t/∂x∂y ²)|_((x,y)=(0,0))=2A,(∂³ t/∂x ² ∂y)|_((x,y)=(0,0))=0,(∂³ t/∂y ³)|_((x,y)=(0,0))=0.

This last constraint slightly restricts the solution, we now require:(∂³ F(y)/∂y ³)|_((x,y)=(0,0))=0.in the thickness formulat=A(xy ²+⅓x ³)+Bx ² +Cxy+Dx+E+F(y)+F1(x,y)x ⁴ +F2(y)x ³ y+F3(y)x ² y ²+F4(y)xy ³.

As an alternative, matched spherical surfaces can be on the inside.After adjustment, the lenses are glued together (preferably withrefractive index matching glue) as a single unit with no air gap. Thisshould provide a superior mechanical structure, and the internalsurfaces are removed, but the optical performance may be somewhatinferior.

Computer Simulations

Various optical designs based on the present invention have been testedwith computer simulations. Specific simulations were made using computeraided design software available from Zemax Development Corporation withoffices in Bellevue, Wash. Several simulations were-made for lens pairswith optical powers of 0 diopter, +2 diopters, and −2 diopters at anglesof 0 degrees, 30 degrees up, 30 degrees down, 30 degrees left and 30degrees right. In all cases the simulations show results that are aboutthe same or better than standard fixed focus prior art spectacle lensesfor correcting focus. Examples of these simulations are discussed abovein the section entitled “ZEMAX Optimization” shown in FIGS. 2A through2C and in FIG. 17.

Variations

The lens can move up and down, side to side, or at any other directionpredominately perpendicular to the wearer's line of sight. The movinglenses for each eye can move in common (best for up and down) or indifferent directions such as out and in away from the nose. Also, bothlenses for each eye can move at the same time in opposite directions.Optimized surfaces can be applied to any of the four surfaces of the twolenses; however, it is best to optimize all of the surfaces.

Lens units of the present invention can be utilized in many applicationsother than for eyeglasses. The concepts can be applied to almost anysituation where adjustable focusing is needed. These includemicroscopes, cameras, copy machines and magnifying glasses.

The present invention can be used for eye examinations. Lateraladjustments can be provided with a micrometer operated by the patient tofocus his eyes at various distances and having a read-out on a computerscreen indicating lens power needed for focusing at those distances.Such devices might be provided at drug stores selling inexpensive lensesfor reading. In addition the lenses might be used to confirm aprescription.

The pivot location does not have to be between the wearer's eyes. Forexample, each lens unit could be designed with a pivot location at theoutside edge of the eyeglasses or at the top or bottom of the lensunits. There may be situations where only one of the lens units of apair of eyeglasses would be designed for an adjustable focus.

Manufacturing techniques that could be employed include: machining (suchas with numerically controlled equipment), molding, casting, curing anduse of gradient index lenses for which thickness is replaced by “opticalpath length” defined by:(n−1)*(thickness)where n is the index of refraction. Potential range finders includeoptical, laser and acoustic. Cues for automatic changing of focus couldinclude blinking, eyebrow motion, head motion, and hand switches.

In the preferred embodiments and in the claims, surface shapes aresometimes defined with mathematical equations. Minor modifications tothe equations can be made without causing variations that couldsignificantly adversely affect the performance of the lens systems.Therefore, in his claims Applicant has used the term “approximately” inconnection with these equations with the intention of claiming systemsthat utilize surfaces that are defined by equations that are not exactlythe same as the referenced equations but achieve the same result withinthe tolerance of the lens system as it is being applied. Also, when herefers to A for one lens element being the complement, or “substantiallythe complement”, of A for the other lens element, he means that theirmagnitudes are so close to each other that any difference results ineffects that are within the tolerance of the lens system to which theequations are being applied. When applied to eyeglasses the applicabletolerance is the ability of the human eye to detect a difference.

The reader should understand that the present invention is not limitedto the specific embodiments described above and that many modificationsand additions or deletions could be made to those described embodiments.Therefore, the scope of the invention should be determined by theappended claims and their legal equivalents.

1. Adjustable focus eyeglasses comprising: A) two lens units, each lensunit comprising a first lens element and a second lens element, and eachlens element having a specially designed thickness profile wherein thedesigns of the thickness profiles are chosen such that small adjustmentsof the relative positions of the two lenses in directions perpendicularor approximately perpendicular to a viewing direction results in changesin the combined focus of the two lenses of the lens unit; B) aneyeglasses frame system for holding said lens elements, said framesystem comprising an adjustment mechanism for adjustment of the positionof at least one of the two lens elements relative to the other in adirection generally perpendicular to a viewing direction; wherein thethickness profiles are approximately given by the following threeequations defining a thickness profile function for each of the two lenselements:((αv+1)⁻²∂³ t/∂u ³+α(αv+1)⁻¹∂² t/∂v∂u)|_((u,v)=(0,0))=2A(∂³ t/∂v ² ∂u)|_((u,v)=(0,0))=2A((αv+1)⁻¹∂³ t/∂v∂u ²−α(αv+1)⁻²∂² t/∂u ²)|_((u,v)=(0,0))=0, where A forone lens element to be the complement, or substantially the complement,of the other lens element and where the thickness profile functionscontinuous, and the derivatives up to at least third order arecontinuous.
 2. The eyeglasses as in claim 1 wherein the solutions to thethickness profile functions are approximately given by:t = [uv² + 2(α  v + 1)(α  u − sin (α  u))/α³] + B[2(α  v + 1)(1 − cos (α  u))/α²)] + C[v  sin (α  u)/α − (α  u − sin (α  u))/α²)] + Du + E + F(v) + F  1(u, v)u⁴ + F  2(v)u³v + F  3(v)u²v² + F  4(v)uv³,where F(v), F1(u,v), F2(v), F3(v) and F4(v) are any functions over thearea of the lenses for which derivatives up to at least third order arecontinuous and at least one of F1(u,v), F2(v), F3(v) and F4(v) is nonzero.
 3. The eyeglasses as in claim 2 wherein said relative motion islinear and the thickness profile functions are approximately given by:(∂³ t/∂x ³)|_((x,y)=(0,0))=2A(∂³ t/∂x∂y ²)|_((x,y)=(0,0))=2A(∂³ t/∂x ² ∂y)|_((x,y)=(0,0))=0. with the solution for each of the twolens elements beingt=A(xy ²+⅓x ³)+Bx ² +Cxy+Dx+E+F(y)+F1(x,y)x ⁴ +F2(y)x ³ y+F3(y)x ² y ²+F4(y)xy ³. where at least one of F1, F2, F3 and F4 is non zero.
 4. Theeyeglasses as in claim 2 wherein said relative motion is pivotal and thethickness profile functions are approximately given by:r ₀ ⁻¹(r ⁻²∂³ t/∂θ ³ +r ⁻¹∂⁷ t/∂r∂θ)|_((r,θ)=(0,0))=2Ar ₀ ⁻¹(∂³ t/∂r ²∂θ)|_((r,θ)=(ro,0))=2Ar ₀ ⁻¹(r ⁻¹∂³ t/∂r∂θ ² −r ⁻²∂² t/∂θ ²)|_((r,θ)=(ro,0))=0. with thesolution for each of the two lens elements being:t=Ar ₀[(r ² +r ₀ ²)θ−2rr ₀ sin(θ)]+B2r ₀ r(1−cos(θ))+Cr ₀ [r sin(θ)−r ₀θ]+Dr ₀ θ+E+F(r)+F1(r,θ)r ₀ ⁴θ⁴ +F2(r)r ₀ ³(r−r ₀)θ³ +F3(r)r ₀ ²(r−r₀)²θ² +F4(r)r ₀(r−r ₀)³∂ where at least one of F1, F2, F3 and F4 are nonzero.
 5. The eyeglasses as in claim 3 wherein parameters and functionsare chosen to optimize at least six lens properties chosen from thefollowing list of lens properties: a. on-axis variable optical power b.off-axis variable optical power c. on-axis residual aberration d.off-axis residual aberration e. magnitude of motion required for thevariable power f. minimum lens thickness g. total weight h. frontsurface appearance i. minimum lens spacing j. maximum lens spacing k.eye to inner surface distance l. eye to outer surface distance m. totalwedge n. variable wedge o. matching of wedge between the eyes p.insensitivity to exact eye location q. prescription base correction r.at least one surface pre-defined to match a stock shape.
 5. Theeyeglasses as in claim 4 wherein parameters and functions are chosen tooptimize at least six lens properties chosen from the following list oflens properties: a. on-axis variable optical power b. off-axis variableoptical power c. on-axis residual aberration d. off-axis residualaberration e. magnitude of motion required for the variable power f.minimum lens thickness g. total weight h. front surface appearance i.minimum lens spacing j. maximum lens spacing k. eye to inner surfacedistance l. eye to outer surface distance m. total wedge n. variablewedge o. matching of wedge between the eyes p. insensitivity to exacteye location q. prescription base correction r. at least one surfacepre-defined to match a stock shape.
 7. The eyeglasses as in claim 3wherein parameters and functions are chosen to optimize at least tenlens properties chosen from the following list of lens properties: a.on-axis variable optical power b. off-axis variable optical power c.on-axis residual aberration d. off-axis residual aberration e. magnitudeof motion required for the variable power f. minimum lens thickness g.total weight h. front surface appearance i. minimum lens spacing j.maximum lens spacing k. eye to inner surface distance l. eye to outersurface distance m. total wedge n. variable wedge o. matching of wedgebetween the eyes p. insensitivity to exact eye location q. prescriptionbase correction r. at least one surface pre-defined to match a stockshape.
 8. The eyeglasses as in claim 4 wherein parameters and functionsare chosen to optimize at least ten lens properties chosen from thefollowing list of lens properties: a. on-axis variable optical power b.off-axis variable optical power c. on-axis residual aberration d.off-axis residual aberration e. magnitude of motion required for thevariable power f. minimum lens thickness g. total weight h. frontsurface appearance i. minimum lens spacing j. maximum lens spacing k.eye to inner surface distance l. eye to outer surface distance m. totalwedge n. variable wedge o. matching of wedge between the eyes p.insensitivity to exact eye location q. prescription base correction r.at least one surface pre-defined to match a stock shape.
 9. Theeyeglasses as in claim 1 wherein said adjustment mechanism is adapted tomove both of the lens elements in each lens unit relative to each otherso as to adjust the focusing power of the lens unit.
 10. The eyeglassesas in claim 1 wherein each of said first and said second lens elementsin said each of said at least one lens unit are fixed relative to eachother after an adjustment of their relative positions in order toproduce a desired combined focusing power.
 11. The eyeglasses of claim 1wherein said adjustment mechanism is adapted to be operated manually.12. The eyeglasses of claim 1 wherein said lens adjustment mechanism isa motor driven lens adjustment mechanism.
 13. The eyeglasses of claim 12wherein said motor driven lens adjustment mechanism is based on ameasured distance to a viewed object.
 14. The eyeglasses of claim 12wherein said motor driven lens adjustment mechanism is based onmeasurements of the wearer's eye positions.
 15. The eyeglasses of claim12 wherein said motor driven lens adjustment mechanism is based onspecial cues from the wearer.
 16. The eyeglasses as in claim 11 whereinsaid adjustment mechanism is adapted to be operated by a finger forceagainst a friction force to slide one lens element in each lens unitrelatively to the other lens element in the lens unit.
 17. Theeyeglasses as in claim 11 wherein said frame system comprises a supportframe and two separate frames holding the lenses and said adjustmentmechanism is adapted to provide a pivot about pivot points on theearpiece of the support frame.
 18. The eyeglasses as in claim 11 whereinsaid frame system comprises a support frame with two earpieces and aseparate frame wherein two rear lenses are mounted in the support frameand two front lenses are mounted in the separate frame and theadjustment mechanism is adapted to provide a pivots of the separateframe about points on the earpieces of the support frame.
 19. Theeyeglasses as in claim 11 wherein said adjustment mechanism comprises apivot bar adapted to produce lateral displacement of the lenses relativeto each other when the torsion bar is twisted.
 20. The eyeglasses as inclaim 11 wherein said adjustment mechanism comprises a guide means forguiding the movement of the lens elements in each lens unit to assurethat the movement of each lens element is in a direction approximatelyperpendicular to a viewing direction.
 21. The eyeglasses as in claim 20wherein said direction maps an arc of a circle defining a lens movementradius.
 22. The eyeglasses as in claim 11 wherein said adjustmentmechanism is adapted to move the two lens elements in each lens unit inopposite directions.
 23. The eyeglasses as in claim 22 wherein saidopposite directions are opposite directions on a curve.
 24. Theeyeglasses as in claim 23 wherein said curve is a circle.
 25. Theeyeglasses as in claim 24 wherein said adjustment also comprises a nosepiece adapted to assure that relative movement of the two lens elementin each lens unit is in opposite directions from a central point. 26.The eyeglasses as in claim 25 wherein said central point isapproximately co-aligned with a line of sight from an eye of a wearer ofthe lens system.
 27. The eyeglasses as in claim 11 wherein saidadjustment mechanism comprises an adjusting element chosen from thefollow group of adjusting elements: (1) a knob, (2) a cam, (3)squeezable off-set arms, (4) a lever, (5) gears, (6) a screw (7) a snapand (8) a spring loaded attachment.
 28. The eyeglasses as in claim 4wherein said adjustment mechanism comprises a pivot mechanism.
 29. Theeyeglasses as in claim 28 wherein said adjustment mechanism furthercomprises four pivot arms each of the four pivot arms connecting onelens element to the one pivot mechanism.
 30. The eyeglasses as in claim29 wherein a front lens element of a right lens unit is rigidlyconnected via two of said four pivot arms and a first pivotable portionof the one pivot mechanism to a rear lens element of a left lens unitand a front lens element of the left lens unit is rigidly connected viatwo of said four pivot arms and a second pivotable portion of the onepivot mechanism to a rear lens element of said right lens unit.
 31. Theeyeglasses as in claim 29 wherein a front lens element of a right lensunit is rigidly connected via two of said four pivot arms and a firstpivotable portion of the one pivot mechanism to a front lens element ofa left lens unit and a rear lens element of the right lens unit isrigidly connected via two of said four pivot arms and a second pivotableportion of the one pivot mechanism to a rear lens element of said leftlens unit.
 32. The eyeglasses as in claim 29 wherein a front lenselement of the right lens unit is pivotably connected via two of saidfour pivot arms and the one pivot mechanism to a rear lens element ofthe right lens unit and a front lens element of the left lens unit ispivotably connected via two of said four pivot arms and the one pivotmechanism to a rear lens element of said left lens unit.
 33. Theeyeglasses as in claim 1 wherein the two lens units define a right lensunit and a left lens unit and the right lens unit defines a right lensunit optical axis and the left lens unit defines a left lens unitoptical axis and said adjustment mechanism comprises a single pivotmechanism located midway between the left lens unit optical axis and theright lens unit optical axis.
 34. The eyeglasses as in claim 28 andfurther comprising at least two finger operated pivot adjustment tabs toadjust the focus of each of the two the lens units.
 35. The eyeglassesas in claim 34 wherein the tabs are adapted to be operated with fingersof one hand.
 36. The eyeglasses as in claim 1 wherein said adjustmentmechanism comprises a motor driven pivot adjustment mechanism.
 37. Theeyeglasses as in claim 28 and further comprising a pivot positionstabilizing means for stabilizing the pivot position of the lenselements at a desired focus.
 38. The eyeglasses as in claim 37 whereinsaid pivot position stabilizing means comprises at least one detent. 39.The eyeglasses as in claim 37 wherein said pivot position stabilizingmeans comprises frictional force means for stabilizing the position byfrictional force.
 40. The eyeglasses as in claim 37 wherein said pivotposition stabilizing means comprises at least one magnet stabilizing theposition by magnetic force.
 41. The eyeglasses as in claim 37 whereinsaid pivot position stabilizing means is incorporated into said pivotadjustment mechanism.
 42. The eyeglasses as in claim 27 and furthercomprising two nose pads with one of said two nose pads is attached toone of said front or rear left lens elements and the other of said nosepads is attached to said front or rear right lens elements.
 43. Theeyeglasses as in claim 1 wherein at least one of said left and rightlens units comprises a static aberration.
 44. The eyeglasses as in claim43 wherein said static aberration is a prescription surface.
 45. Theeyeglasses as in claim 43 wherein the static aberration is applied to asingle surface of the front or rear lens element of said at least onelens unit.
 46. The eyeglasses as in claim 43 wherein the staticaberration is applied to a more than one surface of the front or rearlens element of said at least one lens unit.
 47. The eyeglasses as inclaim 1 wherein each lens element defines a front and rear surface andcomprises a base shape applied to both front and rear surfaces.
 48. Theeyeglasses as in claim 47 wherein the base shape defines a bow.
 49. Theeyeglasses as in claim 1 wherein each lens element comprises a lensdesign code optimized thickness.
 50. The eyeglasses as in claim 1wherein each lens unit comprises a power base to which the specializedcomplementary surfaces are in addition.
 51. The lens system as in claim10 wherein each of said first and said second lens elements in said eachof said two lens unit are fixed relative to each other after anadjustment of their relative positions in order to produce a desiredcombined focusing power and combined astigmatism.
 52. The lens system asin claim 11 wherein said frame system comprises a support frame and twoseparate frames holding the lens elements wherein the adjustmentmechanism is adapted to translate the two separate frames in a primarilyhorizontal direction.
 53. The lens system as in claim 11 wherein saidframe system comprises a support frame for holding two lens elements anda separate frame for holding two lens elements and the adjustmentmechanism is adapted to translate the separate frame with its two lenselements in a primarily horizontal direction.